No abstract

Recent experiments find large differences in binary blend miscibilities between poly(propylene) in its ordinary and head-to-head forms with poly(ethylene propylene). This miscibility variation cannot be understood from simple Flory–Huggins (FH) theory but can readily be explained with the lattice cluster theory (LCT), a generalization of FH theory that accounts for nonrandom mixing, monomer structure, and chain semiflexibility in a systematic manner. Calculations are also presented of miscibility trends for poly(propylene)/poly(ethylene butylene) blends, one of which has yet to be studied. Experiments for this system should provide a nontrivial test of the LCT predictions.

The generalization of the lattice cluster theory (LCT) to include explicit trans-gauche energy differences is applied to study the combined influences of chain stiffness disparities, monomer molecular structures, energetic asymmetries, and nonrandom mixing on the miscibilities of binary polymer blends. The combination of all these relevant physical features within a single theory enables testing various divergent suggestions concerning the dominant physical factors governing the miscibility of polyolefin blends. Thus, tests are presented of models ascribing the observed miscibility patterns in polyolefin blends solely to entropic factors (stiffness disparities) or solely to enthalpic factors (solubility parameter models). The LCT computations demonstrate the combined importance of both factors, as well as several others arising from monomer molecular structures and compressibility. An important and highly nontrivial ingredient in these tests is the novel computation of the mean square radius of gyration for structured monomer chains. The LCT also provides partial tests of a model in which thermodynamically equivalent semiflexible linear chains replace real polyolefin chains. In addition, we extend to semiflexible chains and to asymmetric polymerization indices a remarkable correlation between the binary blend critical temperature and a structural parameter that depends on the fractions of tri-and tetrafunctional united atom groups in the component chains (for model blends in which all van der Waals interactions are equal). Several comparisons with experiment for polyolefin blends serve to explain the molecular origins of observed deviations from solubility parameter models for the phase behavior of blends containing poly(isobutylene), as well as for the observed very weak variation of the critical temperature with molecular weights observed in some experimental blends.

The lattice cluster theory (LCT) is used to determine the essential microscopic parameters that influence the phase separation in binary blends of linear semiflexible lattice chains with equal polymerization indices. The LCT and the polymer reference interaction site model are shown to predict nearly identical and universal constant volume phase behaviors (after simple numerical rescaling of the polymerization indices) for “athermal” blends with vanishing van der Waals attractive energies. Phase separation in these systems is driven solely by stiffness disparities. LCT computations are extended to “thermal” systems in which the van der Waals interactions are large enough to produce liquid densities at standard temperature and pressure. Both the stiffness disparity between the blend components and the relative magnitudes of the van der Waals interaction energies influence the phase behavior of the model blends. We find a family of universal constant volume spinodals, parameterized by the exchange energy. Compressibility is shown to produce significant enthalpic contributions to phase separation, even when all van der Waals energies are identical. We also study the pressure dependence of these model blends, as well as the variety of qualitatively different phase behaviors exhibited. A future work will determine the combined influence of monomer structure, semiflexibility, van der Waals interactions, and the energetic implications of compressibility on the phase behavior of polyolefin blends.

This paper reports single-molecule tracking (SMT) measurements of the diffusion behaviors of individual, anionic sulforhodamine B (SRB) dye molecules in a series of poly­(ethylene oxide) (PEO) films, aimed at clarifying the influences of the molecular weight, network plasticization, and thermal annealing on such dynamics. Micrometer-thick PEO films were prepared by drop-casting from its aqueous (0.2%, 1 nM SRB) solution, followed by drying in air and thermal annealing at 90 °C for 36 h. The diffusion of individual SRB occurring within the amorphous domains was recorded at different relative humidities (5–95%) to characterize the microscale domains’ local aspect-ratio, orientation, and molecular permeability at high spatial resolution. The results revealed the involvement of crystalline phases in confining SRB diffusion to submicron distances and guiding longer-range diffusion along one-dimensional-like amorphous morphologies. Upon annealing, amorphous domains were wider, more continuous, and more permeable to SRB probes. The enhanced transport in plasticized PEO, as reflected by the higher SRB mobility and diffusivity, was linked to the polymer’s higher chain and segmental mobilities and reduced hydrogen-bonding interactions. This work has demonstrated the usefulness of SMT for an advanced characterization of solid polymer electrolytic films, highly beneficial for the development of safer lithium-ion batteries.

Nearest-neighbor pair distribution functions are computed from the semiflexible chain lattice cluster theory (LCT) for binary polymer blends and are compared with the predictions of simple random mixing theory. The LCT treats lattice model polymers with structured monomers and with variable chain flexibility by allowing the monomers to extend over several lattice sites and by introducing trans ↔ gauche bending energies. Comparisons with Monte Carlo simulations for polymer melts enable further tests for the accuracy and limitations of the LCT, while computations of nearest-neighbor pair distribution functions for a variety of binary polyolefin blends provide a link between the phase behavior of these blends and the microscopic local correlations induced by packing constraints and energetic interactions. Altering monomer structures leads to subtle changes in pair distribution functions but profound variations in phase behavior. The calculations of the nearest-neighbor pair distributions provide a simple microscopic explanation for the LCT predictions of the pressure dependence of blend phase diagrams. Variations of the nearest-neighbor pair distribution functions with chain stiffness, van der Waals interactions, temperature, polymerization indices, etc., are correlated with trends in phase behavior and other physical properties. The semiflexible chain LCT is used for further tests towards developing a computationally convenient thermodynamically equivalent linear semiflexible chain model to mimic the melt and blend properties of experimental (or theoretical) structured monomer chains.

We introduce two methods for extending Huggins-Guggenheim-Miller ͑HGM͒-type theories for lattice model polymer chains to describe the dependence of polymer thermodynamic properties on chain architectures ͑e.g., linear, branched, comb, structured monomer chains͒, thereby rectifying a half-century old deficiency of these venerable theories. The first approach is based upon a mathematically precise definition of the ''surface fractions'' that appear in the final HGM random mixing theory. These surface fractions are determined from exact enumerations for short chains, which are found to converge rather rapidly. The approach is illustrated for linear chains, but is readily applied for branched systems. The resultant ''improved'' HGM theory is tested by parameter-free comparisons with Monte Carlo simulations as well as with Flory-Huggins theory, the original HGM theory, and the lattice cluster theory ͑LCT͒. A second improved HGM theory is generated by providing more accurate treatments of the nearest-neighbor pair probabilities that form the basic assumptions and ingredients in, for instance, Guggenheim's derivation of the HGM theory. The more accurate pair probabilities are obtained from the LCT for branched polymer systems ͑or chains with structured monomers͒, and comparisons are again provided with Monte Carlo simulations and previous theories. These comparisons serve to underscore inherent limitations of fundamental assumptions invoked by HGM theories and possible methods for their alleviation. Unfortunately, all simple ''improvements'' of the HGM theory diminish its accuracy, thereby demonstrating that the apparent successes of the HGM theory emerge from a cancellation of errors.

Small-angle neutron scattering ͑SANS͒ experiments have been performed for three polybutadiene/ polystyrene ͑dPB/PS͒ blends of differing dPB microstructure as a function of pressure and temperature. The experimental effective SANS interaction parameters are analyzed using the mean-field lattice cluster theory ͑LCT͒. In order to provide a meaningful comparison with the LCT, contributions from the non-mean-field long-range composition fluctuations are removed from the experimental data by use of a crossover function that describes the transition between near-critical and mean-field behaviors for the extrapolated zero-angle scattering. The theory provides a good description of the overall pressure dependence of the effective interaction parameter and its small dependence on the percentage of 1,2 addition units in the dPB chains.